UniversalCVI (version 1.2.0)

CH.IDX: Calinski–Harabasz (CH) index

Description

Computes the CH (T. Calinski and J. Harabasz, 1974) index for a result either kmeans or hierarchical clustering from user specified kmin to kmax.

Usage

CH.IDX(x, kmax, kmin = 2, method = "kmeans", nstart = 100)

Value

CH

the CH index for k from kmin to kmax shown in a data frame where the first and the second columns are k and the CH index, respectively.

Arguments

x

a numeric data frame or matrix where each column is a variable to be used for cluster analysis and each row is a data point.

kmax

a maximum number of clusters to be considered.

kmin

a minimum number of clusters to be considered. The default is 2.

method

a character string indicating which clustering method to be used ("kmeans", "hclust_complete", "hclust_average", "hclust_single"). The default is "kmeans".

nstart

a maximum number of initial random sets for kmeans for method = "kmeans". The default is 100.

Author

Nathakhun Wiroonsri and Onthada Preedasawakul

Details

The CH index is defined as
$$CH(k) = \frac{n-k}{k-1}\frac{\sum_{i=1}^k|C|_id(v_i,\bar{x})}{\sum_{i=1}^k\sum_{x_j\in C_i}d(x_j,v_i)}$$

The largest value of \(CH(k)\) indicates a valid optimal partition.

References

T. Calinski, J. Harabasz, "A dendrite method for cluster analysis," Communications in Statistics, 3, 1-27 (1974).

See Also

Hvalid, Wvalid, DI.IDX, FzzyCVIs, R1_data

Examples

library(UniversalCVI)

# The data is from Wiroonsri (2024).
x = R1_data[,1:2]

# ---- Kmeans ----

# Compute the CH index
K.CH = CH.IDX(scale(x), kmax = 15, kmin = 2, method = "kmeans", nstart = 100)
print(K.CH)

# The optimal number of cluster
K.CH[which.max(K.CH$CH),]

# ---- Hierarchical ----

# Average linkage

# Compute the CH index
H.CH = CH.IDX(scale(x), kmax = 15, kmin = 2, method = "hclust_average")
print(H.CH)

# The optimal number of cluster
H.CH[which.max(H.CH$CH),]